1. Introduction
Position, Navigation and Timing (PNT) has become important fundamental information for various navigation systems. The Global Navigation Satellite System (GNSS) serves as the primary system supporting PNT in maritime operations today. Recent studies have demonstrated that integrating multiple GNSS constellations, such as GPS, GLONASS and BeiDou, enhances positioning accuracy and reliability in maritime navigation (Zalewski et al., Reference Zalewski, Bąk and Bergmann2022). Furthermore, advancements in real-time kinematic (RTK) positioning techniques have significantly improved the precision of vessel tracking, achieving accuracies within centimetres (Maritime Technology Review, 2024). These developments underscore the critical role of GNSS in providing accurate and reliable PNT information for modern shipping operations. Currently, this GNSS information is transmitted to various places via the Automatic Identification System (AIS). In recent years, the implementation of Satellite-based Automatic Identification Systems (SAT-AIS) has significantly enhanced the ability to monitor maritime traffic on a global scale. Studies have demonstrated the feasibility and effectiveness of SAT-AIS in extending vessel tracking beyond coastal regions, thereby improving maritime domain awareness (Høye et al., Reference Høye, Eriksen, Meland and Narheim2008). Furthermore, the International Maritime Organization (IMO) has recognised the importance of long-range identification and tracking (LRIT) of ships, adopting resolutions to standardise and promote these capabilities (Carson-Jackson, Reference Carson-Jackson2012). Under the current applications of AIS information, seven areas of use have been identified: (1) AIS data mining; (2) navigation safety; (3) ship behaviour analysis; (4) environmental evaluation; (5) trade analysis; (6) ship and port performance; and (7) Arctic shipping (Dong et al., Reference Dong, Lingxiao, Shuaian, Haiying and Kevin2019). Recently, research has been conducted using AIS data to predict ship movements through machine learning (Brian and Lokukaluge, Reference Brian and Lokukaluge2021; Park et al., Reference Park, Jeong and Park2021). In all the aforementioned areas, the PNT information obtained from the AIS data is extremely important. If the position accuracy in the position report (United States Coast Guard, 2021) transmitted from the AIS is 1, the position error is defined to be less than 10 m. However, it is known that vessel positions received by AIS contain error data, and methods for estimating vessel track data from acquired data (Alizadeh et al., Reference Alizadeh, Alesheikh and Sharif2021; Jaskólski et al., Reference Jaskólski, Marchel, Felski, Jaskólski and Specht2021; Yang et al., Reference Yang, Xinqiang, Ling, Jiansen, Qinyou, Xianghui and Ying2021) and for removing noise from AIS data (Sun et al., Reference Sun, Chen, Jun, Zhao, Qinyou, Fang and Yan2021; Chuang et al., Reference Chuang, Songtao, Muzhuang and Yuanchang2023; Jin et al., Reference Jin, Hao, Quan, Xin and Hongdong2023) have been implemented. Furthermore, the reliability structure of AIS is examined by investigating the time intervals between two consecutive AIS position reports received from the same vessel (Jaskólski, Reference Jaskólski2014). According to this, it reports a decrease in reliability when the time interval between two consecutive AIS position reports received from the same vessel exceeds 30 s if the speed is less than 14 knots, exceeds 18 s if the speed is in the range of 14 to 23 knots, or exceeds 6 s if the speed exceeds 23 knots, or if the position error δn at time t exceeds 10 m. When investigating traffic environments using AIS information (Fukuda et al., Reference Fukuda, Tamaru and Shoji2021a; Fukuda and Shoji, Reference Fukuda and Shoji2017; Lee et al., Reference Lee, Lee and Cho2022; Qiang et al., Reference Qiang, Jinxian and Suyi2014), it has been confirmed that it is sometimes difficult to determine the authenticity of position information. For example, as shown in Table 1, the same data are used for the same position, even though the speed is approximately 12 knots and the time difference is 12 s, or the position error is off by several tens of metres from the position estimated from the forward/backward position relationship, regardless of the position accuracy of 1, which is less than 10 m.
Table 1. Examples of received AIS data that may be erroneous
The current AIS time data are based on the time received by a computer or server on the AIS receiver side and time stamp. As the AIS data transmission method is based on the Self Organised Time Division Multiple Access (SOTDMA) method, it can be easily inferred that there is a gap between when a ship acquires its position and when the receiver knows its position, but it is not possible to determine the length of this gap from the current AIS data. Furthermore, to perform an extensive analysis, it is necessary to use AIS data received by multiple receiving stations. When doing this, it is sometimes difficult to delete duplicate data because when multiple AIS receiving stations receive the same information at the same time, there is a slight difference in the time it takes for the data to arrive at the server that processes the data on the line. These problems are likely to be solved if we can know when the vessel acquires the position data. Last et al. (Reference Last, Bahlke, Hering-Bertram and Linsen2014) reported that, in practice, both static and dynamic AIS data are often partially unavailable or incomplete in received messages, and that actual reporting intervals frequently deviate from those specified in the AIS technical standards. Here, ‘availability’ refers to the empirical presence of data in real-world transmissions, rather than the operational readiness defined in IMO resolutions. In the AIS and Very High Frequency Data Exchange System (VDES), which may be used to monitor autonomous vessels in the future, data reliability of positional accuracy is an important factor to improve the safety of navigation. Therefore, it was necessary to verify the accuracy of how the position data differed depending on the time the vessel acquired its position information and when it received the AIS information.
In addition, transmitting roll and pitch data in conjunction with the accurate position estimation time could expand the range of use of AIS data and contribute to safer vessel operation. For example, there have been cases of containers collapsing (Branch, Reference Branch2007); however, it is difficult to determine exactly what kind of hull motion would have caused this problem, unless the ship has its own attitude data such as that on roll and pitch. Although we avoid mentioning individual accidents due to the nature of the information (i.e. human lives), there are many vessels that have capsized due to GM anomalies caused by factors such as improper maintenance of ballast tanks, over-loading, illegal renovations, cargo loading position and hull damage. In the future, online GM estimation (Chhoeung and Hahn, Reference Chhoeung and Hahn2019; Linder et al., Reference Linder, Enqvist, Fossen, Johansen and Gustafsson2015) using roll and pitch data could be used to detect GM anomalies to prevent excessive vessel motion and capsizing accidents. To acquire roll and pitch data, new equipment needs to be installed, but because those data can be acquired by an inertial navigation system and GPS-integrated system (INS/GPS) or an INS and Doppler velocity log integrated system (INS/DVL) using Micro-Electrical Mechanical System (MEMS) Inertial Measurement Unit (IMU) (Fukuda et al., Reference Fukuda, Hatta, Guo and Kubo2021b), data acquisition can be done at low cost. Another advantage of INS/GPS is the ability to acquire data synchronised with GPS time, which contributes to precise timing alignment in multi-sensor systems. While GPS signals are vulnerable to jamming and spoofing, this study focuses on the temporal synchronisation capability (the ‘T’ in PNT), rather than on countermeasures to GNSS interference.
The following investigation was conducted to determine the extent to which the AIS time and position data differed from the reference values and the period of time required to transmit the attitude data. First, we compared the AIS information with the time and position obtained by the Real-Time Kinematic Global Positioning System (RTK-GPS) with 5-Hz output, and we analysed the extent to which the original position differed from that at the time of the AIS reception. The next step was to verify the data-transmission cycle and attitude data (roll and pitch) by generating angular velocity and acceleration data with different sampling periods using the data measured on the ship and comparing them with the reference values using cross-correlation. Furthermore, the actual AIS reception time was used to verify whether the transmission cycle was sufficient by examining the similarity between the angular velocity and acceleration estimated with the current AIS transmission cycle and the signal used as a reference.
The remainder of this paper is organised as follows. Section 2.1 describes the methods used to verify the position error caused by AIS reception time. Moreover, the appropriate AIS data transmission cycle for sending attitude data is described in Section 2.2. Section 3 summarises the results of the verification using the results of the actual experimental voyage; these results are discussed in Section 4. Finally, Section 5 concludes the study.
In this paper, the term ‘reliability’ is used to refer specifically to data reliability, defined as the confidence in the reported AIS data when it matches predefined accuracy criteria. This definition differs from the system-level ‘reliability’ as described in IMO Resolution A.915(22), which concerns uninterrupted system operation over time. Specifically, for AIS position accuracy reported as 1 (with errors less than 10 m), positions derived from received AIS data are considered reliable if they fall within 10 m of the reference position. It should be noted that while GPS position errors themselves contribute to accuracy, this paper does not delve into the discussion of the accuracy of GPS position estimation itself.
2. Methods
2.1. Estimation of the positional error due to differences in time
To investigate the positional error caused by the AIS reception time, the AIS reception time, which consists of the corrected time stamp and position, was compared with the RTK-GPS-obtained time and position. It is worth noting that the UTC (Coordinated Universal Time) seconds received as time stamps are the GPS time at the time of position estimation converted to UTC. In other words, the UTC hour and minute at which the position estimation was performed cannot be assessed from the current AIS-received signal. First, the horizontal distance error of the position was calculated by referring to the same RTK-GPS information as the AIS time. To calculate the horizontal distance error, we used the formula provided by the Geospatial Information Authority of Japan (2013). Next, the time of the RTK-GPS data was adjusted for the AIS position acquired at a certain time to find the RTK-GPS time and position closest to the AIS position. We then stored the amount of time adjustment and the difference in the horizontal position between the RTK-GPS and AIS at this time. The analysis was performed using only those times when the AIS positional accuracy was 1 (United States Coast Guard, 2021).
$$HP{D_{\left( {{T_i}} \right)}} = {\left\{ {{P_{AIS\left( {{T_i}} \right)}} - {P_{RTK\left( {{T_i}} \right)}}} \right\}_{GIAJ}},$$
$$\min \left( {HP{D_{\left( {{T_i}} \right)}}} \right) = {\left\{ {{P_{AIS\left( {{T_i}} \right)}} - {P_{RTK\left( {{T_i} \pm \Delta t} \right)}}} \right\}_{GIAJ'}}$$
where
$HP{D_{\left( {{T_i}} \right)}}$
is the horizontal position difference between AIS and RTK-GPS at time T
i
, output in metres;
$\;{P_{AIS\left( {{T_i}} \right)}}$
is the AIS position with the latitude and the longitude at time T
i
, which is corrected by the time stamp;
$\;{P_{RTK\left( {{T_i}} \right)}}$
is the RTK-GPS position with the latitude and the longitude at time T
i
;
${\left\{ {} \right\}_{GIAJ}}$
indicates that JIAJ is substituted into the formula previously presented by the Geospatial Information Authority of Japan (2013);
$\min \left( {HP{D_{\left( {{T_i}} \right)}}} \right)$
is the PD when RTK-GPS is adjusted for Δt seconds to minimise the PD from the AIS position at time T
i
;
${\Delta t}$
is the amount of time adjustment for RTK-GPS.
For
${P_{RTK\left( {{T_i}} \right)}}$
, the lever arm effect is corrected as
$$_{RTK\left( {{T_i}} \right)} = P'_{RTK\left( {{T_i}} \right)} - {T_r^P} C_N^B Tl_{Ba}^B,$$
$P_{RTK\left( {{T_i}} \right)}^{'}$
, RTK-GPS position before lever arm correction;
$\;l_{Ba}^B$
, lever arm from INS to GNSS antenna;
$\;{\rm{C}}_{\rm{N}}^{\rm{B}}$
, direction cosine matrix, based on roll (ϕ), pitch (θ) and yaw (ψ);
$\;T_r^p$
, transformation matrix based on curvature radii and position
$${\rm{C}}_{\rm{N}}^{\rm{B}} = \left( {\matrix{ 1 & 0 & 0 \cr 0 & {\cos \phi } & {\sin \phi } \cr 0 & { - \sin \phi } & {\cos \phi } \cr } } \right)\left( {\matrix{ {\cos \theta } & 0 & { - \sin \theta } \cr 0 & 1 & 0 \cr {\sin \theta } & 0 & {\cos \theta } \cr } } \right)\left( {\matrix{ {\cos \psi } & {\sin \psi } & 0 \cr { - \sin \psi } & {\cos \psi } & 0 \cr 0 & 0 & 1 \cr } } \right)$$
$$T_r^p = \left( {\matrix{ {{1 \over {{R_N}\left( {{L_b}} \right) + {h_b}}}} & 0 & 0 \cr 0 & {{1 \over {\left( {{R_E}\left( {{L_b}} \right) + {h_b}} \right)\cos {L_b}}}} & 0 \cr 0 & 0 & { - 1} \cr } } \right)$$
$P_{RTK\left( {{T_i}} \right)}^{'}$
is the RTK-GPS position before lever arm effect correction,
$l_{Ba}^B$
is the lever arm from the INS to the GNSS (Global Navigation Satellite System) antenna and
${\rm{C}}_{\rm{N}}^{\rm{B}}$
is direction cosine matrix from Equation (2.22) of Paul (Reference Paul2013). where
$\phi $
is roll,
$\theta $
is pitch and
$\psi $
is yaw at the time
$\left( {{T_i}} \right)$
. Here,
$T_r^p$
is expressed as Equation (5) from Equation (14.104) of Paul (Reference Paul2013), where
${L_b}$
is latitude,
${h_b}$
is altitude,
${R_N}$
is the radius of curvature for north-south motion and
${R_E}$
is the radius of curvature for east-west motion at the time
$\left( {{T_i}} \right)$
.
Finally, the cross-track error and the along-track error is estimated by using following equations:
$$CT{E_{\left( {{T_i}} \right)}} = HP{D_{\left( {{T_i}} \right)}}\sin \left( {{\theta _{AtoR}} - {\theta _{COG}}} \right)$$
$$AT{E_{\left( {{T_i}} \right)}} = HP{D_{\left( {{T_i}} \right)}}\cos \left( {{\theta _{AtoR}} - {\theta _{COG}}} \right)$$
where
${T_{\left( {{T_i}} \right)}}$
is the cross-track error which is the component of the Vessel Technical Error (VTE) perpendicular to the intended track (IMO, 2002).
$AT{E_{\left( {{T_i}} \right)}}$
is the along-track error which is the component of the Vessel Technical Error in the direction of the intended track (IMO, 2002). The VTE is the difference between the indicated craft position and the indicated command or desired position. It is a measure of the accuracy with which the craft is controlled (IMO, 2002). VTE is
$HP{D_{\left( {{T_i}} \right)}}$
in this paper. The
${\theta _{AtoR}}$
is the direction from AIS position to RTK-GPS position. These are illustrated in Figure 1.
Figure 1. Vessel technical error, cross-track error and along-track error.
2.2. Data authenticity verification using different sampling periods
This section describes a method for examining the data-transmission cycle when including roll and pitch data in the AIS data.
2.2.1. Angular velocity and acceleration data generation using INS/GPS/Gyrocompass (IGG)
To avoid loss of data integrity, in the sense of consistency and trustworthiness of estimated motion data across sensors with different accuracies, due to differences in the accuracy of the sensors used, we estimated the angular velocity and acceleration from the data estimated by IGG (Fukuda and Kubo, Reference Fukuda and Kubo2022) in a system based on the Trajectory Generator (Fukuda et al., Reference Fukuda, Hatta and Kubo2021c; Fukuda and Kubo, Reference Fukuda and Kubo2022) and examined the sampling period. Because of the periodicity of vessel roll and pitch data, we avoided correlating and comparing them using attitude data. For example, when comparing rolls, if the values are the same, the correlation will be high. Even if the roll value is the same when compared at one point in time to another, the roll value may decrease or increase. In such cases, the similarity can be confirmed by comparing the angular velocities. The IGG is a composite of the INS, GPS and gyrocompass data with an Extended Kalman filter (Fukuda and Kubo, Reference Fukuda and Kubo2022). By inputting the attitude, position and velocity data obtained from the IGG into a system based on the Trajectory Generator (TG) (Fukuda et al., Reference Fukuda, Hatta and Kubo2021c; Fukuda and Kubo, Reference Fukuda and Kubo2022), the acceleration and angular velocity are estimated at a specified sampling period, as shown in Figure 2. The acceleration and angular velocity obtained by the TG were input to the INS to calculate the estimated position. The position was compared with the position output by the TG to confirm that the error was less than the threshold (0.2 m, in this case) before the system proceeded to the next segment. In this study, the input data sent from the IGG to the TG was set to 1 Hz (1 s), 0.5 Hz (2 s), 0.33 Hz (3 s), 0.25 Hz (4 s), 0.2 Hz (5 s), 0.17 Hz (6 s) and 0.1 Hz (10 s), because we wanted to compare and study these data with those from the update cycle of the AIS. For this input, the output of the acceleration and angular velocity estimated by the TG was set to 1 Hz as shown in Figure 2.
Figure 2. Estimation of acceleration and angular velocity by using input values from INS/GPS/Gyrocompass (IGG) to Trajectory Generator (TG).
2.2.2. Acceleration and angular velocity data generation using AIS data
This section describes a method for the TG estimation of acceleration and angular velocity using AIS data. Pure AIS data, which is to be verified in this study, contains the difference between when the vessel acquires its position and when the AIS receiver receives the data based on the characteristics of the receiving system. Therefore, to clarify the relationship between the update time of the data and the acceleration and angular velocity, which we are trying to clarify in this study, we only used the time calculated from the time stamp and the AIS data reception time. Acceleration and angular velocity were estimated by simultaneously inputting IGG data (position, attitude and velocity) with the AIS reception time into the TG. Although the current AIS data do not include attitude (roll and pitch) data, the estimated acceleration and angular velocity, including attitude, were used for comparison in this study. Figure 3 shows a schematic of the estimation process.
Figure 3. Estimation of acceleration and angular velocity by using input values from IGG to TG according to AIS reception time.
2.2.3. Acceleration and angular velocity data comparison
The cross-correlation coefficients (Math Works. Measuring Signal Similarities (1) (Math Works, 2024a)) and p-values (Math Works. Linear or Rank Correlation (2) (Math Works, 2024b)) of MATLAB were used to compare the acceleration and angular velocity. The actual measurements of the IMU contained errors that were composed of deterministic and stochastic parts (Petko and Tsonyo, Reference Petko and Tsonyo2010). Furthermore, in the case of MEMS sensors, temperature also had a significant impact (Mohammed et al., Reference Mohammed, Ahmed and Spiros2006). Therefore, to avoid including these errors, the 1-Hz data estimated by the TG were used as the reference sensor value. For the p-value, if the p-value was less than 0.05, the hypothesis of no correlation existing between the two types of data was rejected (Math Works. Linear or Rank Correlation (2)). Generally, for correlation coefficients 0 to less than 0.3, 0.3 to less than 0.5, 0.5 to less than 0.7, 0.7 to less than 0.9 and 0.9 or more, there was almost no correlation, very weak correlation, normal correlation, strong correlation and very strong correlation, respectively.
3. Experimental outline and results
The Shioji Maru shown in Figure 4 is a training ship with LOA = 49.93 m, a beam of 10.00 m, a draft of 3.80 m, a gross tonnage of 425 tons, a main engine of 1400 PS at 700 rpm, a variable pitch propeller, a bow thruster of 2.4 tonnes and a stern thruster of 1.8 tonnes. The RTK-GPS antenna was installed on the port (left) side of the bridge roof and its position is indicated by the yellow dotted line in Figure 4. Furthermore, during the experiments, the third-generation Shioji Maru was used, but the current Shioji Maru has been updated to the fourth generation. IMU, GPS, RTK-GPS and Gyrocompass data were acquired on the training ship Shioji Maru belonging to the Tokyo University of Marine Science and Technology on October 4, 2019 (experimental voyage 1, EV1; Figure 5a), March 3, 2021 (experimental voyage 2, EV2; Figure 5b) and July 16, 2021 (experimental voyage 3, EV3; Figure 5c). The reference point for the reported position of the Shioji Maru was confirmed by AIS Message 5 (to port, 4 m; to starboard, 6 m; to bow, 15 m; and to stern, 34 m; this position was on the bridge) and the RKT-GPS was also installed on the bridge. On the same day, the AIS data received on land were also acquired. Figure 5 shows the track of the Shioji Maru during each experimental voyage with the full voyage track (white), the track used for the analysis in Section 3.1 (red) and the track used for the analysis in Section 3.2 utilisation section (green). The specifications based on catalogue values for the equipment used are shown in Tables 2 and 3.
Figure 4. Training Ship Shioji Maru III.
Figure 5. Tracks for experimental voyages (a) 1, (b) 2 and (c) 3.
Table 2. Sensor information
Table 3. Specifications of the TG-5000 gyrocompass
3.1. Estimating the difference between GPS position acquisition time and AIS reception time, and the corresponding position error
We used AIS data collected by the Advanced Navigational Center at Tokyo University of Marine Science and Technology for EV1 and EV3. For EV2, we purchased AIS data from a Japanese company that sold it to major research institutes in Japan. As the AIS receiving server reception time affects the analysis results, one AIS dataset was purchased from a well-known vendor. Accordingly, the analysis results described hereon were obtained using data from at least two AIS data-receiving servers, namely, the one installed at the Tokyo University of Marine Science and Technology and the one installed in the vendor’s AIS data-receiving station. To distinguish the temporal errors and GPS positioning errors, only data on speeds of more than 4 m/s and no sudden turns were analysed. The along-track error was expressed as ATE. The ATE and SOG (Speed Over the Ground) of the ship without time correction for EV1–3 are shown in Figures 6a, 6d and 6g, respectively, while Figures 6b, 6e and 6h show the cross-track error. Also, Figures 6c, 6f and 6i show the ATEs and the Amount of Reception Time Adjustment (ARTA) after adjusting the RTK time so that the ATE between the AIS and RTK would be minimised.
Figure 6. ATEs and Speed Over Ground (SOG) before the AIS reception time adjustment, Cross-Track Error and Receiving Time Adjustment and Amount of Reception Time Adjustment after AIS reception time adjustment for experimental voyages 1, 2 and 3. ATE, Along-track error; ATEA, maximum ATEs after receiving time adjustment; ARTA, Amount of Reception Time Adjustment.
For EV1–3, the maximum ATEs before correction were 79.7 m (SOG 4.7 m/s), 117.1 m (SOG 6.1 m/s) and 85.1 m (SOG 5.6 m/s), respectively. The maximum values of the ARTA were 16.8, 19.5 and 16 s, respectively, representing the times when the maximum ATE was observed. When the ATE in EV1–3 was maximum, the errors after time adjustment were 0.5, 5.0 and 1.5 m, respectively. The maximum ATEs after receiving time adjustment (ATEA) were 10.7, 21.3 and 10.0 m for Figures 5b, 5d and 5f, respectively, all of which were observed at different times from the time of the maximum ATE before time adjustment. In addition, the average ATEs before the time adjustment were 10.3, 13.8 and 11.9 m, respectively. The average ATEAs were 2.9, 6.4 and 3.5 m, respectively. It can be seen from Figures 5b, 5d and 5f that, in all the experimental observations, points with an ATEA of more than 10 m were observed after the time adjustment.
In EV1–3, the time used for estimation, the amount of data, the percentage of data whose AIS position accuracy was 1, the percentage of data whose difference from RTK was less than 10 m and the percentage of data whose difference from RTK was less than 10 m after time adjustment are shown in Table 4. In Experiment 2, wherein AIS data purchased from a vendor were used, the percentage of data with a position accuracy of 1 was as low as 48.6% of the total, that with a position accuracy of 1 and an accuracy of 10 m or less was 61.6% to 70.5% of the total before the time adjustment, and that after the reception time adjustment exceeded 87% of the total in all the experiments.
Table 4. AIS data collected from experimental voyages (EVs) 1, 2 and 3
The relationship among ATE, SOG and ARTA is shown in Figure 7. Figures 7a, 7c and 7e show the relation between ATE and SOG times ARTA. The differences are also shown in Figures 6d, 6h and 6l. As can be seen from Figures 7a, 7c and 7e, the position error (in metres) before time adjustment and the time adjustment and SOG product are consistent, with differences of less than 10 m, as shown in Figures 7b, 7d and 7f, and averages of 2.2, 4.8 and 5.1 m, respectively. In Figures 7a, 7c and 7e, the areas where ATE is 0 and
${\rm{SOG}} \times {\rm{ARTA}}$
is a sloping line (non-zero) are times with no AIS data.
Figure 7. ATEs before the AIS reception time adjustment and Speed Over Ground (SOG) times Amount of Receiving Time Adjustment (ARTA) and their differences for experimental voyages 1, 2 and 3.
3.2. Acceleration and angular velocity data verification with different sampling periods
This section evaluates the validity of acceleration and angular velocity data derived via the TG method by comparing it with reference data under various sampling conditions. Subsection 3.2.1 discusses the estimation of 1-Hz reference values using the TG and compares them with actual IMU measurements. Subsection 3.2.2 investigates how the correlation between estimated and measured values varies with different sampling frequencies. Subsection 3.2.3 examines the estimation accuracy using AIS reception times. Each analysis focuses on the correlation coefficients and p-values to assess the reliability of the TG method under diverse temporal conditions.
3.2.1. Estimation of the 1-Hz reference value via TG and comparison with the measured value
The data were sampled at 1 Hz from the IGG data for 90 min for EV1–3, and the TG was used to estimate the acceleration and angular rate sensor values at 1 Hz. The correlation coefficients and p-values between these estimated values and the actual data acquired by the IMU are shown in Table 5. The average correlation coefficients through EV1–3 were 0.80, 0.66 and 0.91 for the angular rate sensor values on the X-, Y- and Z-axes, respectively, and 0.43, 0.85 and 0.72 for the acceleration sensor values on the X-, Y- and Z-axes, respectively. The p-values were all 0. Due to the influence of the 0.5 Hz GPS correction in IGG, the correlation coefficient for the X-axis acceleration was lower than that of the other axes.
Table 5. Correlation coefficients and p-values between TG estimated values at 1 Hz and actual IMU output
3.2.2. Correlation coefficient and p-value verification for each sampling frequency
We sampled data at 1, 0.5, 0.3 (3 s), 0.25, 0.2, 0.17 (6 s), 0.1 and 0.05 Hz from the 90-min IGG data for EV1–3, and we used the TG to estimate the angular rate and accelerometer values at 1 Hz with and without attitude (roll, pitch). The maximum and average horizontal ATEs in the INS position according to the TG values at each sampling period and the IGG are shown in Figures 8a and 8b, respectively. In the figure, ‘NRP’ is the abbreviation for ‘no roll pitch’. A lower sampling frequency is associated with a larger error with the IGG. There is no significant difference between the estimation with and without attitude. This is because the TG estimated the acceleration to be closer to the position of the IGG even in the no attitude case, which does not necessarily mean that the acceleration is accurately estimated (i.e. NRP fails to consider the value effect of gravity acceleration in the horizontal axis, which has significant effect on the accelerometer output).
Figure 8. Difference between the estimated position by pure inertial navigation and that by the IGG in each sampling period.
Tables 6 and 7 show the average values and p-values of the correlation coefficients of EV1–3 at each frequency of the angular velocity and acceleration. The correlation coefficients and p-values for each axis from EV1–3 are shown in Appendix A. No p-value was greater than 0.05 for any axis, and no correlation was denied by the p-value. As for the angular velocity, there was a strong correlation in all the axes up to the 0.5 Hz sampling frequency. For the X-axis, there was a correlation up to 0.25 Hz, but almost no correlation after 0.2 Hz. For the Y-axis, there was a correlation up to 0.33 Hz, but no correlation after 0.25 Hz. For the Z-axis, there was a strong or very strong correlation at all frequencies, and with the roll and pitch input, it was the same as it was without the input.
Table 6. Correlation coefficients and p-values compared with TG-estimated angular velocity at 1 Hz
NRP, no roll or pitch.
Table 7. Correlation coefficients and p-values compared with TG-estimated acceleration at 1 Hz
As for the acceleration, with the roll and pitch input, the X-axis showed correlation up to 0.33 Hz, the Y-axis showed correlation in all the frequency bands and the Z-axis showed correlation only at 0.5 Hz. In the absence of the roll and pitch input, the X- and Z-axes were correlated up to 0.5 Hz, and the Y-axis was correlated in all the frequency bands. Comparing the conditions with and without the roll and pitch input, the values of the correlation coefficients for the X- and Y-axes were higher than they were with the input, while the values for the Z-axis were almost the same under both conditions.
3.2.3. Estimated correlation coefficient and p-value verification according to AIS reception time
In EV1–3, AIS data were acquired, and the angular velocity and acceleration were estimated via TG. As described in Section 3.1, there is a difference between the time when the vessel estimated its position and the time of position estimation examined from the received data by the AIS receiver. Therefore, we estimated the angular velocity and acceleration at 1 Hz from the time of the AIS data reception, and the position and attitude of the IGG at that time using the TG. The amount of data, time and update time (average, median, maximum and minimum values) of the AIS data used in this study are summarised in Table 8. The nominal interval for the AIS at 0–14 knots was 10 s during the navigation, and 3 and 1/3 s during the changing course (IALA, 2016; IEC, 2001; ITU, 2014). Here, 80.4%, 83.6% and 73.5% of the data from EV1–3, respectively, followed the nominal interval. The AIS data that did not follow this interval for any reason were 19.4%, 16.3% and 26.3% of the data from EV1–3, respectively. To complement the average (AVE) values and provide a more robust representation of the central tendency of the data, the median (MED) values for each speed interval were also calculated and are presented in Table 8. As MED is less sensitive to outliers, it offers an additional perspective on the typical duration observed in each interval. In this study, the MED values (9, 9 and 10 s) closely align with the AVE values (7.8, 7.4 and 8.9 s), suggesting that the data distribution is relatively stable and that extreme values had limited impact on the results.
Table 8. Summary of the AIS data used
Table 9 summarises the correlation coefficients and p-values of the angular velocity and acceleration estimated by the TG using the time of the AIS reception and the IGG data at that time, compared with the reference value of 1 Hz. The average correlation coefficients of the angular velocities for EV1–3 were 0.24, 0.19 and 0.85 for the X-, Y- and Z-axes, respectively. The average of the Z-axis angular velocity without the roll and pitch input was 0.85. Except for the Z-axis angular velocity, the results were almost uncorrelated. The average correlation coefficients of the acceleration were 0.28, 0.63 and 0.16 for the X-, Y- and Z-axes, respectively, and 0.11, 0.43 and 0.16 without the roll and pitch input. Only the Y-axis acceleration showed a correlation. As for the p-values of the angular velocity and acceleration, they were all zero and the p-value was below the significance level of 0.05, so the hypothesis that there was no correlation between the two columns was rejected.
Table 9. Summary of the correlation coefficients and p-values of the angular velocity and acceleration estimated by the TG using the AIS reception time and IGG data
4. Discussion
We took the RTK-GPS position as a reference for the AIS position and investigated the horizontal distance error caused from using the AIS reception time. Comparing the RTK positions with the positions at the time of the AIS reception for EV1–3, it was found that even when the positional accuracy was 1 (position error is less than 10 m), which was obtained by the AIS position report (United States Coast Guard, 2021), there were horizontal errors of up to 79.7 m (SOG 4.7 m/s), 117.1 m (SOG 6.1 m/s) and 85.1 m (SOG 5.6 m/s) for EV1–3, respectively. At these points, the RTK-GPS reception time at which the horizontal error with the AIS position was minimised was examined, and the differences with the AIS time were 16.8, 19.5 and 16 s, respectively. The product of this time difference and speed was 79.8, 117.0 and 85.6 m, respectively, which was almost the same as the horizontal error before time correction. Figure 6 shows that this trend is consistent for all time correction points. As shown in Table 4, after applying the time correction, the horizontal position errors for EV1, EV2 and EV3 were less than 10 m 99.0%, 87.2% and 100.0% of the time, respectively. As the horizontal error was reduced to less than 10 m via time correction, this error was considered to arise from the position estimation time estimated based on the AIS reception time and time stamp being different from the actual position estimation time. The main causes of time lag are old AIS information remaining in slots when receiving AIS information at land stations and old AIS information being received via AIS relay stations. Since the satellite VDES receives a wider range of information, using the same method as that for AIS signals may not remove old AIS information and may make location information more unreliable. This result showed that, when transmitting information by the AIS or VDES, it is necessary to transmit the information in such a way that the receiver knows the GNSS time (such as GPS time) when the vessel acquires its position. More accurate position interpolation (Dennis et al., Reference Dennis, Arne and Axel2021) and position estimation using AIS data would be possible if accurate position estimation times were known. We believe that a difference in distance of approximately 110 m is not a problem when the navigator is on board and constantly monitoring the ship; such factors are not such a problem during operation. However, in a system that remotely and automatically monitors multiple autonomous vessels, the timing of risk calculations and anti-collision warnings is expected to be affected. In the AIS data used in EV2 (purchased from a vendor), the same position was found to be stored at different times. The vendor explained that this was an error that occurred when combining data that were received from multiple receiving stations. Such data duplication can cause confusion in the monitoring of ships including autonomous vessels, and it is necessary to remove the duplicated data by using position estimation time such as the GPS time.
Next, to investigate the data-transmission cycle when including attitude data (roll and pitch) for monitoring autonomous ships, we estimated the angular velocity and acceleration using the TG and verified them using the correlation coefficients. It was found that a data-transmission cycle of at least 0.5 Hz (2 s) was necessary to estimate and correlate the angular velocity and acceleration. We also verified the results with and without the roll and pitch inputs. This revealed that the correlation coefficient for the X- and Y-axis accelerations were higher with the roll and pitch input. This is because the effect of gravity acceleration can be removed by taking posture into account. For the Z-axis angular velocity, the presence of the roll and pitch had no effect. This was because the Z-axis angular velocity was corrected by the Gyrocompass. It is also clear from Figure 7 that the horizontal error between the IGG and TG increases as the sampling time increases, although it is limited to the TG-based method. Last et al. (Reference Last, Bahlke, Hering-Bertram and Linsen2014) concluded that it was difficult to implement motion models and collision avoidance algorithms based solely on AIS data because current prediction algorithms rely on short fixed-time intervals. There is a good possibility that the AIS or VDES could be used in collision avoidance for vessels if the update period was more than 0.5 Hz (corresponding to a sampling interval of 2 s); this was revealed by examining the correlation coefficient of the angular velocity and acceleration with respect to ship motion. It should be noted that radar and ARPA remain as important as they have been.
Finally, in EV1–3, the angular velocity and acceleration were estimated by the TG using the time of AIS reception and the IGG data at that time. The data were compared with the reference data to determine if similarity of the angular rate and acceleration data could be obtained at the current AIS transmission cycle. As a result, we found that only the Z-axis angular velocity and Y-axis acceleration were correlated; however, it is difficult to obtain a correlation between acceleration and angular velocity in all axes from the current AIS reception interval. As for acceleration, the correlation coefficient was higher when the posture data were inputted. For the Y-axis acceleration, we obtained the average of the correlation coefficients of acceleration, when the sampling frequency was 4 s or more, as shown in Appendix A, and we found that they were 0.85, 0.47 and 0.64, respectively, which were almost identical to the correlation coefficients of 0.83, 0.44 and 0.62 for the AIS, as shown in Table 9. The same could be said for the angular velocity and acceleration of the other axes. This result also shows that if we want to obtain data with high correlation coefficients for the AIS, we need to increase the amount of data for frequencies above 0.5 Hz (2 s).
5. Conclusions
Assuming that AIS and VDES systems will be used in the future for vessel monitoring, including autonomous vessel monitoring, traffic control, GM estimation, accident analysis and various other studies, we examined the reliability of the current AIS data position accuracy and the cycle of attitude data transmission. The results showed that even if the positional accuracy of the AIS data was indicated to be 1 (i.e. position error is less than 10 m), there would be a horizontal error due to the difference in time between when the position was viewed at the receiver’s time and when it was acquired by the ship using the GNSS. Furthermore, it was shown that the original positioning accuracy could be obtained by performing time correction. In conclusion, it is desirable to add the time when the ship estimates its position (GPS time, etc.) to the position information transmitted from the ship for increasing position data reliability. The sampling frequency at which attitude data had to be transmitted was studied by estimating the angular velocity and acceleration using the TG in INSs and examining the correlation coefficient. It was found that the correlation between the angular velocity and acceleration could be obtained if a sampling frequency of 0.5 Hz or more was achieved. Finally, we estimated the angular velocity and acceleration from the current AIS-received data and verified them by correlating them. As a result, it was found that it was difficult to correlate the angular rate and acceleration under the current AIS communication conditions, even when attitude data such as roll and pitch were included. In other words, although the TG-based method proposed in this study can reproduce angular rate and acceleration when the data update frequency exceeds 0.5 Hz, the current AIS data transmission rate is lower than this threshold. Therefore, it is not feasible to reliably estimate ship motion using the existing AIS system.
Since GNSS equipment is installed on almost all AIS-equipped ships, the inclusion of GNSS time in AIS data is an issue that can be immediately discussed for introduction without the need for additional equipment. Accidents involving vessels cause enormous damage not only to human lives but also to the environment. Thus, we strongly believe that this study will contribute to the improvement of AIS data reliability and vessel safety, thereby reducing the number of vessel accidents.
Author contributions
Gen Fukuda Conceptualisation, Methodology, Software, Validation, Formal analysis, Investigation, Writing – Original Draft, Funding acquisition; Hitoi Tamaru: Methodology, Formal analysis, Validation, Formal analysis, Writing – Review & Editing; Nobuaki Kubo: Methodology, Software, Validation, Formal analysis, Resources, Writing – Review & Editing; Ruri Shoji: Methodology, Writing - Review & Editing, Supervision.
Funding statement
This work was supported by the JSPS KAKENHI [grant numbers JP 18K13960 and JP 22 K04550]. The funding agency had no role in study design; in the collection, analysis and interpretation of data; in the writing of the report; and in the decision to submit the paper for publication.
Competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Appendix A
Cross-correlation coefficients and p-values when comparing the estimated angular velocity and acceleration at 1 Hz and other frequencies estimated by the TG are shown in Table A1 and Table A2, respectively.
Table A1. Cross-correlation coefficients and p-values of angular velocity at each frequency obtained from the TG
Table A2. Cross-correlation coefficients and p-values of acceleration at each frequency obtained from the TG
Open access
